mvnormal.py 文件源码

def logpdf(X, Mu, Sigma):
  """Multivariate normal log pdf."""
  # This is the multivariate normal log pdf for an array X of n
  # outputs, an array Mu of n means, and an n-by-n positive-definite
  # covariance matrix Sigma.  The direct-space density is:
  #
  #     P(X | Mu, Sigma)
  #       = ((2 pi)^n det Sigma)^(-1/2)
  #         exp((-1/2) (X - Mu)^T Sigma^-1 (X - Mu)),
  #
  # We want this in log-space, so we have
  #
  #     log P(X | Mu, Sigma)
  #     = (-1/2) (X - Mu)^T Sigma^-1 (X - Mu) - log ((2 pi)^n det Sigma)^(1/2)
  #     = (-1/2) (X - Mu)^T Sigma^-1 (X - Mu)
  #         - (n/2) log (2 pi) - (1/2) log det Sigma.
  #
  n = len(X)
  assert X.shape == (n,)
  assert Mu.shape == (n,)
  assert Sigma.shape == (n, n)
  assert np.all(np.isfinite(X))
  assert np.all(np.isfinite(Mu))
  assert np.all(np.isfinite(Sigma))

  X_ = X - Mu
  covf = _covariance_factor(Sigma)

  logp = -np.dot(X_.T, covf.solve(X_)/2.)
  logp -= (n/2.)*np.log(2*np.pi)
  logp -= covf.logsqrtdet()

  # Convert 1x1 matrix to float.
  return float(logp)